Do you have a heart for this?

Calculus Level 3

x 2 + ( y − x 2 3 ) 2 = 1 \large x^2 + \left ( y-\sqrt[3]{x^2}\right ) ^2 = 1

What is the area enclosed by the above curve?

Who figured out what the title referred to?


The answer is 3.14.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

Michael Mendrin
Sep 18, 2016

Solving for y y gets us

y = x 2 3 ± 1 − x 2 y={ x }^{ \frac { 2 }{ 3 } }\pm \sqrt { 1-{ x }^{ 2 } }

so that the area between the curves is just that of an unit circle, with an area of π \pi

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Did you figure out what the title referred to?

Sharky Kesa - 4 years, 9 months ago

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The graph is that of a heart !

neelesh vij - 4 years, 9 months ago

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Yep! Pretty cool, huh?

Sharky Kesa - 4 years, 9 months ago

How do you know that "is just that of an unit circle" is true?

Pi Han Goh - 4 years, 8 months ago

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The difference is the equation for the unit circle.

Michael Mendrin - 4 years, 8 months ago

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